Algebra: Chapter 0 is a self-contained introduction to the main
topics of algebra, suitable for a first sequence on the subject at the
beginning graduate or upper undergraduate level. The primary
distinguishing feature of the book, compared to standard textbooks in
algebra, is the early introduction of categories, used as a unifying
theme in the presentation of the main topics. A second feature consists
of an emphasis on homological algebra: basic notions on complexes are
presented as soon as modules have been introduced, and an extensive last
chapter on homological algebra can form the basis for a follow-up
introductory course on the subject. Approximately 1,000 exercises both
provide adequate practice to consolidate the understanding of the main
body of the text and offer the opportunity to explore many other topics,
including applications to number theory and algebraic geometry.
This will allow instructors to adapt the textbook to their specific
choice of topics and provide the independent reader with a richer
exposure to algebra. Many exercises include substantial hints, and
navigation of the topics is facilitated by an extensive index and by
hundreds of cross-references.

An obvious question: why another graduate algebra
book? Aren't there all but too many already? Is there anything
genuinely novel to be done when it comes to educating fledgling
graduate students in this subject, given such an already
well-populated and high-quality field? Well, the answer is yes. And
the title of the book under review, Algebra: Chapter 0, is already a
clue to what the author, Paolo Aluffi, is up to. In a perhaps
Bourbakian sense, the prevailing motivation and objective is to
present the subject at hand in a manner that pays proper due to
relatively new foundations, making for a rather different orientation
and flavor for what ensues. ...His treatment of these preliminaries is
thorough as well as eminently accessible: Aluffi writes well, clearly
and engagingly. This characterizes all of Algebra: Chapter 0,
actually, and makes it easy to recommend the book enthusiastically
even aside from the fact that I am a big fan of category theory to
begin with.

-- MAA Online

This self-contained introduction is suitable for a
first sequence at the beginning graduate or upper undergraduate
level. A distinguishing feature of the book is the early introduction
of categories, used as a unifying theme.